Polymerization extent

Vf is the relative volume of the rubber phase, % C is the mean size of dispersed rubber particles X is the polybutadiene content (6+ 2%) X2 is the polymerization temperature at the first stage (120+ lO C) X3 is the polymerization extent after the first stage completion (50+ 15%) X4 is the concentration of n-lauryl mercaptan... 

PCL can have several polymerization extent based on the polymerization method. The mechanical properties of PCL are listed in Table 4.16 (LACTEL PCL 2013). 

Raman spectroscopy has been used extensively in the polymer area for many years and its application has been summarized in several books and review articles over the years [13,15,35-38]. The application of Raman spectroscopy to polymers allows the user to obtain information on general molecular raicrostructure [13,39-44], polymerization (extent and kinetics), copolymer composition [45-49], polymer density [50], molecular weight, hydrogenation [51], degree of unsaturation, morphology including orientation [13,15], tac-... 

The radiation and temperature dependent mechanical properties of viscoelastic materials (modulus and loss) are of great interest throughout the plastics, polymer, and rubber from initial design to routine production. There are a number of laboratory research instruments are available to determine these properties. All these hardness tests conducted on polymeric materials involve the penetration of the sample under consideration by loaded spheres or other geometric shapes [1]. Most of these tests are to some extent arbitrary because the penetration of an indenter into viscoelastic material increases with time. For example, standard durometer test (the "Shore A") is widely used to measure the static "hardness" or resistance to indentation. However, it does not measure basic material properties, and its results depend on the specimen geometry (it is difficult to make available the identity of the initial position of the devices on cylinder or spherical surfaces while measuring) and test conditions, and some arbitrary time must be selected to compare different materials. 

The interaction between ions of the same sign is assumed to be a pure hard sphere repulsion for r < a. It follows from simple steric considerations that an exact solution will predict dimerization only if i < a/2, but polymerization may occur for o/2 < L = o. However, an approximate solution may not reveal the fiill extent of polymerization that occurs in a more accurate or exact theory. Cummings and Stell [ ] used the model to study chemical association of uncharged atoms. It is closely related to the model for adliesive hard spheres studied by Baxter [70]. 

When propene is polymerized under free radical conditions the polypropylene that results IS atactic Catalysts of the Ziegler-Natta type however permit the preparation of either isotactic or syndiotactic polypropylene We see here an example of how proper choice of experimental conditions can affect the stereochemical course of a chemical reaction to the extent that entirely new materials with unique properties result... 

By line 5, the reaction has reached 80% completion and the number average value of the degree of polymerization is 5. Although we have considered this slowly evolving polymer in terms of the extent of reaction, another question starts to be worrisome How long is this going to take ... 

The question posed in Sec. 5.2-how long will it take to reach a certain extent of reaction or degree of polymerization —is now answered. As is often the case, the answer begins, It all depends. . . . ... 

In this section we turn our attention to two other questions raised in Sec. 5.2, namely, how do the molecules distribute themselves among the different possible species and how does this distribution vary with the extent of reaction Since a range of species is present at each stage of the polymerization, it is apparent that a statistical answer is required for these questions. This time, our answer begins, On the average. . . . ... 

One distinction that should be pointed out involves the comparison of Eqs. (5.1) and (5.40). In the former we considered explicitly the AB monomer, while the latter is based on the polymerization of AA and BB monomers. In both instances is obtained by dividing the total number of monomer molecules initially present by the total number of chains after the reaction has occurred to extent p. Following the same procedure for different reaction... 

Assuming that 0.5 mol % of the diol is lost to polymerization by dehydration to olefin, what would be the value of if the reaction were carried out to the same extent as in (1) ... 

We noted above that the presence of monomer with a functionality greater than 2 results in branched polymer chains. This in turn produces a three-dimensional network of polymer under certain circumstances. The solubility and mechanical behavior of such materials depend critically on whether the extent of polymerization is above or below the threshold for the formation of this network. The threshold is described as the gel point, since the reaction mixture sets up or gels at this point. We have previously introduced the term thermosetting to describe these cross-linked polymeric materials. Because their mechanical properties are largely unaffected by temperature variations-in contrast to thermoplastic materials which become more fluid on heating-step-growth polymers that exceed the gel point are widely used as engineering materials. 

What we seek next is a quantitative relationship between the extent of the polymerization reaction, the composition of the monomer mixture, and the point of gelation. We shall base our discussion on the system described by reaction (5.U) other cases are derived by similar methods. To further specify the system we assume that A groups limit the reaction and that B groups are present in excess. Two parameters are necessary to characterize the reaction mixture ... 

Equation (5.47) is of considerable practical utility in view of the commercial importance of three-dimensional polymer networks. Some reactions of the sort we have considered are carried out on a very large scale Imagine the consequences of having a polymer preparation solidify in a large and expensive reaction vessel because the polymerization reaction went a little too far Considering this kind of application, we might actually be relieved to know that Eq. (5.47) errs in the direction of underestimating the extent of reaction at... 

As an example of the quantitative testing of Eq. (5.47), consider the polymerization of diethylene glycol (BB) with adipic acid (AA) in the presence of 1,2,3-propane tricarboxylic acid (A3). The critical value of the branching coefficient is 0.50 for this system by Eq. (5.46). For an experiment in which r = 0.800 and p = 0.375, p = 0.953 by Eq. (5.47). The critical extent of reaction, determined by titration, in the polymerizing mixture at the point where bubbles fail to rise through it was found experimentally to be 0.9907. Calculating back from Eq. (5.45), the experimental value of p, is consistent with the value =0.578. 

For a fixed extent of reaction, the presence of multifunctional monomers in an equimolar mixture of reactive groups increases the degree of polymerization. Conversely, for the same mixture a lesser extent of reaction is needed to reach a specified with multifunctional reactants than without them. Remember that this entire approach is developed for the case of stoichiometric balance. If the numbers of functional groups are unequal, this effect works in opposition to the multifunctional groups. 

This situation seems highly probable for step-growth polymerization because of the high activation energy of many condensation reactions. The constants for the diffusion-dependent steps, which might be functions of molecular size or the extent of the reaction, cancel out. 

This situation is expected to apply to radical termination, especially by combination, because of the high reactivity of the trapped radicals. Only one constant appears which depends on the diffusion of the polymer radicals, so it cannot cancel out and may be the source of a dependence of the rate constant on the extent of reaction or degree of polymerization. 

Throughout this section we have used mostly p and u to describe the distribution of molecular weights. It should be remembered that these quantities are defined in terms of various concentrations and therefore change as the reactions proceed. Accordingly, the results presented here are most simply applied at the start of the polymerization reaction when the initial concentrations of monomer and initiator can be used to evaluate p or u. The termination constants are known to decrease with the extent of conversion of monomer to polymer, and this effect also complicates the picture at high conversions. Note, also, that chain transfer has been excluded from consideration in this section, as elsewhere in the chapter. We shall consider chain transfer reactions in the next section. 

A moment s reflection reveals that the effect on v of transfer to polymer is different from the effects discussed above inasmuch as the overall degree of polymerization is not decreased by such transfers. Although transfer to polymer is shown in one version of Eq. (6.84), the present discussion suggests that this particular transfer is not pertinent to the effect described. Investigation of chain transfer to polymer is best handled by examining the extent of branching in the product. We shall not pursue the matter of evaluating the transfer constants, but shall consider instead two specific examples of transfer to polymer. 

Inhibitors and retarders differ in the extent to which they interfere with polymerization, and not in their essential activity. An inhibitor is defined as a substance which blocks polymerization completely until it is either removed or consumed. Thus failure to totally eliminate an inhibitor from purified monomer will result in an induction period in which the inhibitor is first converted to an inert form before polymerization can begin. A retarder is less efficient and merely slows down the polymerization process by competing for radicals. 

Figure 7.8 Mole fractions styrene (Mj) and methyl methacrylate (M2) in feedstock (f) and copolymers (F) as a function of the extent of polymerization. Average copolymer compositions are also shown. [From V. E. Meyer and R. K. S. Chan, Polym. Prepr. 8 209(1967), used with permission.]...

To the extent that the data allow, suggest where these substituents might be positioned in Table 7.3. The following reactivity ratios describe the polymerization of acrylonitrile (Ml) with the monomers listed ... 

There is nothing unique about the placement of this isolated segment to distinguish it from the placement of a small molecule on a lattice filled to the same extent. The polymeric nature of the solute shows up in the placement of the second segment This must be positioned in a site adjacent to the first, since the units are covalently bonded together. No such limitation exists for independent small molecules. To handle this development we assume that each site on the lattice has z neighboring sites and we call z the coordination number of the lattice. It might appear that the need for this parameter introduces into the model a quantity which would be difficult to evaluate in any eventual test of the model. It turns out, however, that the z s cancel out of the final result for, so we need not worry about this eventuality. 

The presence of stable free radicals in the final polycondensate is supported by the observation that traces of (11) have a strong inhibiting effect on the thermal polymerization of a number of vinyl monomers. Radical polymerization was inhibited to a larger extent by a furfural resin than by typical polymerization inhibitors (34). Thermal degradative methods have been used to study the stmcture of furfural resinifted to an insoluble and infusible state, leading to proposed stmctural features (35). 

Nxylylene system, substituents affect it only to a minor extent. AH parylenes are expected to have a similar molar enthalpy of polymerization. An experimental value for the heat of polymerization of Parylene C has appeared. Using the gas evolution from the Hquid nitrogen cold trap to measure thermal input from the polymer, and taking advantage of a peculiarity of Parylene C at — 196°C to polymerize abmptiy, perhaps owing to the arrival of a free radical, a = —152 8 kJ/mol (—36.4 2.0 kcal/mol) at — 196°C was reported (25). The correction from — 196°C to room temperature is... 

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